Transcript 4.7 Identity and Inverse Matrices

4.7 Identity and
Inverse Matrices
What is an identity?
In math the identity is the number you multiply by to have
equivalent numbers.
For multiplication it is one.
5 * 1 = 5, of course. How is this useful?
3
If you need to have a denominator of 40 in the fraction
8
3 5 15
 
8 5 40
What is an inverse?
The inverse is a number when multiplied by
another number equals one.
1
4 1 4
4    1
4
1 4 4
4 9 36
 
1
9 4 36
The identity matrix is a square
matrix with one down the diagonals
In a 2 X 2
1 0
0 1 


In a 3 X 3
1 0 0
0 1 0 


0 0 1
Find the matrices that when multiply
together are the identity matrix.
How do we find the inverse?
? ?  2 8 1 0


? ?  1 3 0 1

 
 

Find the inverse
Find the determinant of
 2 8
 1 3


6 – ( - 8) = 14
We will flip the diagonal of top left and bottom
right, then change the signs the bottom left to
top right diagonal.
 2 8
3  8
 1 3  1 2 




Putting the part together
Take the determinant and put it under one
and multiply it by the moved matrix.
1 3  8


14 1 2 
Lets see if it works
1 3  8  2 8



14 1 2   1 3
1  6  8 24  24 1 14 0 
 


14 2  2 8  6  14  0 14
1 0 


0
1


Can there be matrices without
inverses?
Yes, when the determinate equals zero.
  4 6
 2 3  (12  (12))  0


Since a fraction can not have zero for a
denominator. There would be no inverse.
Homework
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